import geopandas as gpd
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
pd.set_option('display.max_columns', 500)
For this lab we return to Fire Service Coverage seeking to assess tradeoffs in service against costs of maintaining different levels of stations.
Instead of covering all demand, the modeling approach tries to maximize the demand covered.
Specifically, we will employ the maximal covering location problem.
Instead of minimizing the number of facilities needed in a previous lab, we now introduce a parameter, $p$, representing a fixed number of facilities to keep in the system.
In Lab 4, there are three research questions we want to look into.
The coverage standard for this lab will be fixed at 8000m.
S = 8000
# Note: it might take time, as FD is a huge file.
FDs = gpd.read_file("/Users/ezrabanks/Desktop/Lab4/Data/California_Fire_Districts.shp")
blocks = gpd.read_file("/Users/ezrabanks/Desktop/Lab4/Data/sbBlocks_pop.shp")
stations = gpd.read_file("/Users/ezrabanks/Desktop/Lab4/Data/Fire_Stations_SBC.shp")
blocks = blocks.to_crs(crs = FDs.crs)
stations = stations.to_crs(crs = FDs.crs)
There are many Fire Districts in California.
We are only going to focus in the "Santa Barbara County Fire District".
In the second map, note that there are many other Fire Districts in Santa Barbara County.
Though it's not shown on the map, they have some overlapping area, which means the area is co-operated by multiple Fire Districts.
FDs.plot("Name")
<Axes: >
FDs = FDs.loc[FDs.intersects(blocks.unary_union)].reset_index(drop=True)
FDs.plot("Name", legend=True, figsize=(10,10))
<Axes: >
SBC_FD = FDs[FDs["Name"] == "SANTA BARBARA CFD"]
SBC_FD
| OBJECTID | County | FDID | MACSID | Name | Address | City | Zip | FireChief | Phone | Notes | LastUpdate | Website | CALFIREUni | SHAPE_Leng | SHAPE_Area | geometry | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 4 | 318 | SANTA BARBARA | 42035 | SBC | SANTA BARBARA CFD | 4410 CATHEDRAL OAKS RD | SANTA BARBARA | 93110 | MARK A. HARTWIG | (805) 681‐5500 | None | 2018-06-21 | https://www.sbcfire.com/ | SBC | 778360.396807 | 3.666998e+09 | MULTIPOLYGON (((23728.804 -401033.857, 23715.3... |
We do this because FDs contains a large shapefile, which might burden your RAM.
del FDs
NOTE: don't forget to RESET_INDEX() whenever you take a subset!
stations = stations[stations.within(SBC_FD.geometry.unary_union)].reset_index(drop = True)
len(stations)
28
Hint: when there's something you don't know about plot function, refer to this document page (https://geopandas.org/en/stable/docs/reference/api/geopandas.GeoDataFrame.plot.html)! Also, you can Google or ask chatGPT :)
blocks['geometry'] = blocks['geometry'].centroid
blocks = blocks[blocks.within(SBC_FD.geometry.unary_union)].reset_index(drop = True)
fig, ax = plt.subplots(figsize=(10, 10))
blocks.plot(column='Population', ax=ax, legend=True, cmap = 'viridis', figsize = fig, alpha = 0.4, markersize=blocks['Population']*0.8)
stations.plot(ax=ax, color='red', label='Stations')
<Axes: >
len(blocks)
3224
len(stations)
28
Decision Variables: \begin{align*} & x_j = \begin{cases} 1, & \text{if facility $j$ is open}, \\ 0, & \text{otherwise}. \end{cases} \\ & y_i = \begin{cases} 1, & \text{if demand $i$ is covered}, \\ 0, & \text{otherwise}. \end{cases} \end{align*}
Parameters: \begin{align*} & I = \text{number of demands}, \\ & J = \text{number of facilities}, \\ & S = \text{Coverage Distance Standard}, \\ & a_i = \text{Weight assigned to demand $i$}, \\ & D_{ij} = \text{Distance between demand $i$ and facility $j$}, \\ & N_i = \{ j \in J \, | \, D_{ij} \leq S \}, \\ & P = \text{the number of facilities to be opened}. \end{align*}
Objective Function: \begin{align*} \text{Maximize:} \quad & \sum_{i=1}^{I} a_i y_i \end{align*}
Constraints: \begin{align*} \text{Subject to:} \quad & \sum_{j \in N_i} x_j \geq y_i, \quad \forall i \in I \\ & \sum_{j=1}^{J} x_j \leq P, \\ & x_j, y_i \in \{0, 1\}, \quad \forall i, j. \end{align*}
I = len(blocks)
J = len(stations)
P = 20
a_i = blocks["Population"]
D_ij = np.array([[blocks.geometry[i].distance(stations.geometry[j]) for j in range(J)] for i in range(I)])
D_ij.shape
(3224, 28)
# This is a hint for students who want to do it with list comprehension
# Creating a two-dimensional list
matrix = [[1, 2, 3],
[4, 5, 6],
[7, 8, 9],
[10, 11, 12]]
# Using list comprehension to filter even numbers from the matrix
# The '%' symbol in Python is called the modulo operator.
#It returns the remainder of the division of the left operand by the right operand.
even_numbers = [[matrix[r][c] for c in range(len(matrix[0])) if matrix[r][c]%2 == 0]
for r in range(len(matrix))]
print(even_numbers)
[[2], [4, 6], [8], [10, 12]]
N_i = [[j for j in range(J) if D_ij[i][j] <= S] for i in range(I)]
import gurobipy as gp
from gurobipy import GRB
# Create a new Gurobi model
mclp = gp.Model("Maximal_Covering_Location")
# Decision Variables
x = mclp.addVars(I, vtype=gp.GRB.BINARY, name="x")
y = mclp.addVars(I, vtype=gp.GRB.BINARY, name="y")
# Objective Function
mclp.setObjective(gp.quicksum(a_i[i] * y[i] for i in range(I)), GRB.MAXIMIZE)
# Constraints
# Each demand must be covered by neighboring facility
mclp.addConstrs((gp.quicksum(x[j] for j in N_i[i]) >= y[i] for i in range(I)))
# Number of opened facilities must not exceed P
mclp.addConstr(gp.quicksum(x[j] for j in range(J)) <= P)
# Optimize the model
mclp.optimize()
Set parameter Username Academic license - for non-commercial use only - expires 2025-05-10 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros Model fingerprint: 0x8394f29b Variable types: 0 continuous, 6448 integer (6448 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 3e+03] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3225 rows and 6448 columns Presolve time: 0.02s Presolve: All rows and columns removed Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.00 work units) Thread count was 1 (of 4 available processors) Solution count 2: 167606 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
open_stations = [j for j in range(J) if x[j].X > 0.5]
open_stations = stations.iloc[open_stations].reset_index(drop=True)
open_stations
| Label | Desig | Number | Type | Department | Name_other | Address | Notes | Num_2019 | Scale | Latitude | Longitude | geometry | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | VAFB-42 | AFV-2 | 42 | Fire Station | Vandenberg Fire Department | None | New Mexico Ave., Vandenberg, CA | None | 42 | 0 | 34.7345 | -120.534 | POINT (-48865.923 -364526.814) |
| 1 | VAFB-44 | AFV-4 | 44 | Fire Station | Vandenberg Fire Department | None | Arguello Rd., Vandenberg, CA | None | 44 | 0 | 34.6125 | -120.570 | POINT (-52227.109 -378048.804) |
| 2 | SBC-31 | SBC-31 | 31 | Fire Station | Santa Barbara County Fire Department | None | 168 W Hwy 246, Buellton, CA 93427 | None | 31 | 900 | 34.6132 | -120.197 | POINT (-18043.064 -378107.359) |
| 3 | SBC-30 | SBC-30 | 30 | Fire Station | Santa Barbara County Fire Department | None | 1644 Oak St., Solvang, CA 93464 | None | 30 | 900 | 34.5935 | -120.142 | POINT (-12980.623 -380307.178) |
| 4 | SBC-32 | SBC-32 | 32 | Fire Station | Santa Barbara County Fire Department | None | 906 Airport Rd., Santa Ynez, CA 93460 | None | 32 | 1100 | 34.6075 | -120.069 | POINT (-6364.715 -378763.420) |
| 5 | SBC-13 | SBC-13 | 13 | Fire Station | Santa Barbara County Fire Department | None | 4570 Hollister, Santa Barbara, CA 93110 | None | 13 | 1000 | 34.4386 | -119.780 | POINT (20241.872 -397479.331) |
| 6 | SBC-27 | SBC-27 | 27 | Fire Station | Santa Barbara County Fire Department | None | 41 Newsome St., New Cuyama, CA 93254 | None | 27 | 700 | 34.9457 | -119.682 | POINT (29023.176 -341164.220) |
| 7 | LPF-35 | LPF-35 | 35 | Fire Station | LPF | Pine Canyon | 8145 Hwy 166, Santa Maria, CA 93454 | None | 35 | 0 | 35.0294 | -120.194 | POINT (-17696.745 -331903.082) |
| 8 | SBC-23 | SBC-23 | 23 | Fire Station | Santa Barbara County Fire Department | None | 5003 Depot Ave., Santa Maria, CA 93454 | None | 23 | 600 | 34.8666 | -120.294 | POINT (-26898.330 -349956.970) |
| 9 | SBC-24 | SBC-24 | 24 | Fire Station | Santa Barbara County Fire Department | None | 99 Centennial, Los Alamos, CA 93440 | None | 24 | 800 | 34.7451 | -120.280 | POINT (-25603.519 -363453.395) |
| 10 | SBC-26 | SBC-26 | 26 | Fire Station | Santa Barbara County Fire Department | None | 1600 Tiffany Park Court, Santa Maria, CA 93455 | None | 26 | 600 | 34.8657 | -120.402 | POINT (-36721.414 -350025.728) |
| 11 | SBC-21 | SBC-21 | 21 | Fire Station | Santa Barbara County Fire Department | None | 335 Union Ave., Orcutt, CA 93455 | None | 21 | 600 | 34.8644 | -120.444 | POINT (-40540.132 -350149.951) |
| 12 | SBC-34 | SBC-34 | 34 | Fire Station | Santa Barbara County Fire Department | None | 3510 Harris Grade Rd., Lompoc, CA 93436 | None | 34 | 1000 | 34.6909 | -120.447 | POINT (-40958.522 -369401.362) |
| 13 | VAFB-43 | AFV-3 | 43 | Fire Station | Vandenberg Fire Department | None | El Rancho Rd., Vandenberg, CA | None | 43 | 0 | 34.7882 | -120.565 | POINT (-51640.364 -358544.456) |
| 14 | SBC-12 | SBC-12 | 12 | Fire Station | Santa Barbara County Fire Department | None | 5330 Calle Real, Goleta, CA 93117 | None | 12 | 900 | 34.4429 | -119.812 | POINT (17256.190 -397008.608) |
| 15 | SBC-11 | SBC-11 | 11 | Fire Station | Santa Barbara County Fire Department | None | 6901 Frey Way, Goleta, CA 93117 | None | 11 | 700 | 34.4258 | -119.870 | POINT (11934.816 -398917.392) |
| 16 | SBC-38 | SBC-38 | 38 | Fire Station | Santa Barbara County Fire Department | None | 17200 Mariposa Reina, Gaviota, CA 93117 | None | 38 | 800 | 34.4767 | -120.214 | POINT (-19690.488 -393256.876) |
| 17 | SBC Camp 1 | SBC-CR | None | Camp | Santa Barbara County Fire Department | Cachuma Camp | Lakeview Dr., Lake Cachuma, CA | Crew 10, Crew 11 | CREW | 1200 | 34.5688 | -119.948 | POINT (4737.414 -383052.783) |
| 18 | CHU-1 | CHU-1 | 1 | Fire Station | Chumash Fire Department | Chumash | 3300 Hwy 246, Santa Ynez, CA 93460 | None | 1 | 0 | 34.6088 | -120.089 | POINT (-8141.257 -378616.310) |
coverage_buffers = open_stations.geometry.buffer(S)
fig, ax = plt.subplots(figsize=(10, 10))
blocks.plot(column='Population', ax=ax, legend=True, cmap='viridis', alpha=0.4, markersize=blocks['Population']*0.8)
open_stations.plot(ax=ax, color='red', label='Open Stations')
SBC_FD.plot(ax=ax, markersize=5, zorder=2, facecolor="none", edgecolor="black")
coverage_buffers.plot(ax=ax, edgecolor='black', linestyle='--', linewidth=1, facecolor="none")
plt.legend()
plt.show()
Here, we will functionize our optimization model.
Sothat with given P value, the model can be solved.
# Let me give you functionize example.
# For more, refer to Lab 0.
sample_list = [1,2,3,4]
def sum_array(a):
s = 0
a = np.array(a)
for num in a:
s += num
return s, a # Return the summation of all elements, and the original array
sum_array(sample_list)
(10, array([1, 2, 3, 4]))
## PUT YOUR FUNCTION HERE!!!##
def solve_mclp(P):
import gurobipy as gp
from gurobipy import GRB
# Create a new Gurobi model
mclp = gp.Model("Maximal_Covering_Location")
# Decision Variables
x = mclp.addVars(I, vtype=gp.GRB.BINARY, name="x")
y = mclp.addVars(I, vtype=gp.GRB.BINARY, name="y")
# Objective Function
mclp.setObjective(gp.quicksum(a_i[i] * y[i] for i in range(I)), GRB.MAXIMIZE)
# Constraints
# Each demand must be covered by neighboring facility
mclp.addConstrs((gp.quicksum(x[j] for j in N_i[i]) >= y[i] for i in range(I)))
# Number of opened facilities must not exceed P
mclp.addConstr(gp.quicksum(x[j] for j in range(J)) <= P)
# Optimize the model
mclp.optimize()
open_stations = [j for j in range(J) if x[j].X > 0.5]
open_stations = stations.iloc[open_stations].reset_index(drop=True)
return open_stations,mclp.obj_val
Current coverage is the sum of all the demand weights, currently covered by existing stations.
Here are the thought process you can go through.
current_coverage = open_stations.buffer(distance = S)
current_coverage = current_coverage.unary_union
current_coverage = blocks.within(current_coverage)
covered_blocks = blocks.loc[current_coverage]
covered_blocks_sum = covered_blocks["Population"].sum()
current_coverage = covered_blocks_sum
current_coverage
167606
current_coverage = stations.buffer(distance = S)
current_coverage = fishnet_points[fishnet_points.geometry.within(current_coverage.unary_union)].reset_index(drop=True)
sum_current = len(current_coverage)
selecteds = [] # List to store selected stations for each value of p
obj_vals = [] # List to store objective values for each value of p
# Iterate over values of p starting from 3
for p in range(3, len(stations)+1):
print(f"=================== for P={p}") # Print current value of p
# Call solve_mclp function to solve the problem for current value of p
selected_stations, obj_val = solve_mclp(p)
# Append selected stations to the selecteds list
selecteds.append(selected_stations)
# Append objective value to the obj_vals list
obj_vals.append(obj_val)
=================== for P=3
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xfbb69dab
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [3e+00, 3e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 28463.000000
Root relaxation: objective 1.420460e+05, 27 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 142046.00000 142046.000 0.00% - 0s
Explored 1 nodes (27 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 142046 28463 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.420460000000e+05, best bound 1.420460000000e+05, gap 0.0000%
=================== for P=4
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x74a1aab2
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [4e+00, 4e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 35944.000000
Root relaxation: objective 1.535990e+05, 20 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 153599.00000 153599.000 0.00% - 0s
Explored 1 nodes (20 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 153599 35944 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.535990000000e+05, best bound 1.535990000000e+05, gap 0.0000%
=================== for P=5
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x41ce3697
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [5e+00, 5e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 101213.00000
Root relaxation: objective 1.578710e+05, 19 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 157871.00000 157871.000 0.00% - 0s
Explored 1 nodes (19 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 157871 101213 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.578710000000e+05, best bound 1.578710000000e+05, gap 0.0000%
=================== for P=6
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x205c5f99
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [6e+00, 6e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 103347.00000
Root relaxation: objective 1.615640e+05, 16 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 161564.00000 161564.000 0.00% - 0s
Explored 1 nodes (16 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 161564 103347 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.615640000000e+05, best bound 1.615640000000e+05, gap 0.0000%
=================== for P=7
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x9e88aae7
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [7e+00, 7e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 138503.00000
Root relaxation: objective 1.636980e+05, 14 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 163698.00000 163698.000 0.00% - 0s
Explored 1 nodes (14 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 163698 138503 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.636980000000e+05, best bound 1.636980000000e+05, gap 0.0000%
=================== for P=8
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x6f496596
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [8e+00, 8e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139069.00000
Root relaxation: objective 1.656950e+05, 11 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 165695.00000 165695.000 0.00% - 0s
Explored 1 nodes (11 simplex iterations) in 0.09 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 165695 139069 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.656950000000e+05, best bound 1.656950000000e+05, gap 0.0000%
=================== for P=9
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xb870dc24
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [9e+00, 9e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139439.00000
Root relaxation: objective 1.663330e+05, 11 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 166333.00000 166333.000 0.00% - 0s
Explored 1 nodes (11 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 166333 139439 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.663330000000e+05, best bound 1.663330000000e+05, gap 0.0000%
=================== for P=10
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x1e198654
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139558.00000
Root relaxation: objective 1.668990e+05, 6 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 166899.00000 166899.000 0.00% - 0s
Explored 1 nodes (6 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 166899 139558 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.668990000000e+05, best bound 1.668990000000e+05, gap 0.0000%
=================== for P=11
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xce9ccc4f
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 140196.00000
Root relaxation: objective 1.671390e+05, 6 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 167139.00000 167139.000 0.00% - 0s
Explored 1 nodes (6 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 167139 140196 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.671390000000e+05, best bound 1.671390000000e+05, gap 0.0000%
=================== for P=12
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x75c48cb7
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 140425.00000
Root relaxation: objective 1.673330e+05, 3 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 167333.00000 167333.000 0.00% - 0s
Explored 1 nodes (3 simplex iterations) in 0.08 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 167333 140425 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.673330000000e+05, best bound 1.673330000000e+05, gap 0.0000%
=================== for P=13
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xd97f63fc
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167360.00000
Root relaxation: objective 1.674520e+05, 2 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 167452.00000 167452.000 0.00% - 0s
Explored 1 nodes (2 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 167452 167360 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.674520000000e+05, best bound 1.674520000000e+05, gap 0.0000%
=================== for P=14
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x172f26d6
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.04s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167374.00000
Root relaxation: objective 1.675220e+05, 2 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 167522.00000 167522.000 0.00% - 0s
Explored 1 nodes (2 simplex iterations) in 0.14 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 167522 167374 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.675220000000e+05, best bound 1.675220000000e+05, gap 0.0000%
=================== for P=15
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xcd36c397
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167443.00000
Root relaxation: objective 1.675910e+05, 1 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 167591.00000 167591.000 0.00% - 0s
Explored 1 nodes (1 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 167591 167443 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.675910000000e+05, best bound 1.675910000000e+05, gap 0.0000%
=================== for P=16
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x354d63a9
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167605.00000
Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 2: 167605 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.676050000000e+05, best bound 1.676050000000e+05, gap 0.0000%
=================== for P=17
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xe7e25a44
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3203 rows and 6407 columns
Presolve time: 0.02s
Presolved: 22 rows, 41 columns, 90 nonzeros
Found heuristic solution: objective 167606.00000
Variable types: 0 continuous, 41 integer (41 binary)
Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.01 work units)
Thread count was 4 (of 4 available processors)
Solution count 2: 167606 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=18
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x85b62fa8
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3210 rows and 6414 columns
Presolve time: 0.01s
Presolved: 15 rows, 34 columns, 62 nonzeros
Found heuristic solution: objective 167606.00000
Variable types: 0 continuous, 34 integer (34 binary)
Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.01 work units)
Thread count was 4 (of 4 available processors)
Solution count 2: 167606 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=19
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xb50fdd7a
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.01s
Presolve: All rows and columns removed
Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)
Solution count 2: 167606 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=20
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x8394f29b
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.02s
Presolve: All rows and columns removed
Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)
Solution count 2: 167606 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=21
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x5da5f73e
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.02s
Presolve: All rows and columns removed
Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)
Solution count 2: 167606 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=22
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x25d04cef
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.01s
Presolve: All rows and columns removed
Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)
Solution count 2: 167606 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=23
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x0c7cae08
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.01s
Presolve: All rows and columns removed
Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)
Solution count 2: 167606 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=24
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x53d33e31
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.01s
Presolve: All rows and columns removed
Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)
Solution count 2: 167606 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=25
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x7ea4a4ef
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.01s
Presolve: All rows and columns removed
Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)
Solution count 2: 167606 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=26
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x5c8dcf4c
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.01s
Presolve: All rows and columns removed
Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)
Solution count 2: 167606 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=27
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x14058442
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.02s
Presolve: All rows and columns removed
Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)
Solution count 2: 167606 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=28
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x7fc3c448
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3225 rows and 6448 columns
Presolve time: 0.01s
Presolve: All rows and columns removed
Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)
Solution count 2: 167606 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
results = pd.DataFrame({
'P': range(3, len(stations)+1),
'Coverage': obj_vals
})
results
| P | Coverage | |
|---|---|---|
| 0 | 3 | 540.0 |
| 1 | 4 | 704.0 |
| 2 | 5 | 855.0 |
| 3 | 6 | 1005.0 |
| 4 | 7 | 1146.0 |
| 5 | 8 | 1270.0 |
| 6 | 9 | 1384.0 |
| 7 | 10 | 1475.0 |
| 8 | 11 | 1564.0 |
| 9 | 12 | 1647.0 |
| 10 | 13 | 1715.0 |
| 11 | 14 | 1743.0 |
| 12 | 15 | 1763.0 |
| 13 | 16 | 1780.0 |
| 14 | 17 | 1789.0 |
| 15 | 18 | 1793.0 |
| 16 | 19 | 1797.0 |
| 17 | 20 | 1797.0 |
| 18 | 21 | 1797.0 |
| 19 | 22 | 1797.0 |
| 20 | 23 | 1797.0 |
| 21 | 24 | 1797.0 |
| 22 | 25 | 1797.0 |
| 23 | 26 | 1797.0 |
| 24 | 27 | 1797.0 |
| 25 | 28 | 1797.0 |
current_coverage
4065
def scatterplot_result(results):
# Plot the DataFrame, in scatter plot, taking P values as x and Coverage values as y
results.plot(kind="scatter", x="P", y="Coverage")
# Add grid lines
plt.grid(True)
# Add the current coverage point in color red
plt.scatter(len(stations), sum_current, color="red")
# provide a dashed red line to inform current coverage
plt.axhline(y=sum_current, color='r', linestyle='--', label='Current Coverage')
# show the plot!
plt.show()
scatterplot_result(results)
Feel free to edit any other plotting details
def map_result(p, demand_block=True):
####My answer
open_stations = selecteds[p-3]
coverage_buffers = open_stations.geometry.buffer(S)
fig, ax = plt.subplots(figsize=(10, 10))
#blocks.plot(column='Population', ax=ax, legend=True, cmap='viridis', alpha=0.4, markersize=blocks['Population']*0.8)
open_stations.plot(ax=ax, color='red', label='Open Stations', zorder = 5000)
SBC_FD.plot(ax=ax, markersize=5, zorder=200, facecolor="none", edgecolor="black")
coverage_buffers.plot(ax=ax, edgecolor='black', linestyle='--', linewidth=1, facecolor="none")
#plt.legend()
#plt.show()
####
if demand_block:
blocks.plot("Population", ax=ax, legend=True, markersize=5)
else:
fishnet_points.plot(ax=ax, zorder = 100)
plt.title(f"{p} stations open")
plt.show()
map_result(10) # Try different p!
def optimize_and_evaluate(demand_block=True):
selecteds = []
obj_vals = []
for p in range(3, len(stations)+1):
print(f"=================== for P={p}")
selected_stations, obj_val = solve_mclp(p)
selecteds.append(selected_stations)
obj_vals.append(obj_val)
map_result(p, demand_block)
results = pd.DataFrame({
'P': range(3, len(stations)+1),
'Coverage': obj_vals
})
scatterplot_result(results)
optimize_and_evaluate()
=================== for P=3
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xfbb69dab
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [3e+00, 3e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 28463.000000
Root relaxation: objective 1.420460e+05, 27 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 142046.00000 142046.000 0.00% - 0s
Explored 1 nodes (27 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 142046 28463 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.420460000000e+05, best bound 1.420460000000e+05, gap 0.0000%
=================== for P=4
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x74a1aab2
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [4e+00, 4e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 35944.000000
Root relaxation: objective 1.535990e+05, 20 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 153599.00000 153599.000 0.00% - 0s
Explored 1 nodes (20 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 153599 35944 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.535990000000e+05, best bound 1.535990000000e+05, gap 0.0000%
=================== for P=5
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x41ce3697
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [5e+00, 5e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 101213.00000
Root relaxation: objective 1.578710e+05, 19 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 157871.00000 157871.000 0.00% - 0s
Explored 1 nodes (19 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 157871 101213 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.578710000000e+05, best bound 1.578710000000e+05, gap 0.0000%
=================== for P=6
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x205c5f99
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [6e+00, 6e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 103347.00000
Root relaxation: objective 1.615640e+05, 16 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 161564.00000 161564.000 0.00% - 0s
Explored 1 nodes (16 simplex iterations) in 0.08 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 161564 103347 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.615640000000e+05, best bound 1.615640000000e+05, gap 0.0000%
=================== for P=7
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x9e88aae7
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [7e+00, 7e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 138503.00000
Root relaxation: objective 1.636980e+05, 14 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 163698.00000 163698.000 0.00% - 0s
Explored 1 nodes (14 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 163698 138503 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.636980000000e+05, best bound 1.636980000000e+05, gap 0.0000%
=================== for P=8
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x6f496596
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [8e+00, 8e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139069.00000
Root relaxation: objective 1.656950e+05, 11 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 165695.00000 165695.000 0.00% - 0s
Explored 1 nodes (11 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 165695 139069 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.656950000000e+05, best bound 1.656950000000e+05, gap 0.0000%
=================== for P=9
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xb870dc24
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [9e+00, 9e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139439.00000
Root relaxation: objective 1.663330e+05, 11 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 166333.00000 166333.000 0.00% - 0s
Explored 1 nodes (11 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 166333 139439 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.663330000000e+05, best bound 1.663330000000e+05, gap 0.0000%
=================== for P=10
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x1e198654
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 139558.00000
Root relaxation: objective 1.668990e+05, 6 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 166899.00000 166899.000 0.00% - 0s
Explored 1 nodes (6 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 166899 139558 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.668990000000e+05, best bound 1.668990000000e+05, gap 0.0000%
=================== for P=11
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xce9ccc4f
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 140196.00000
Root relaxation: objective 1.671390e+05, 6 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 167139.00000 167139.000 0.00% - 0s
Explored 1 nodes (6 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 167139 140196 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.671390000000e+05, best bound 1.671390000000e+05, gap 0.0000%
=================== for P=12
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x75c48cb7
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.02s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 140425.00000
Root relaxation: objective 1.673330e+05, 3 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 167333.00000 167333.000 0.00% - 0s
Explored 1 nodes (3 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 167333 140425 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.673330000000e+05, best bound 1.673330000000e+05, gap 0.0000%
=================== for P=13
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xd97f63fc
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167360.00000
Root relaxation: objective 1.674520e+05, 2 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 167452.00000 167452.000 0.00% - 0s
Explored 1 nodes (2 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 167452 167360 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.674520000000e+05, best bound 1.674520000000e+05, gap 0.0000%
=================== for P=14
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0x172f26d6
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167374.00000
Root relaxation: objective 1.675220e+05, 2 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 167522.00000 167522.000 0.00% - 0s
Explored 1 nodes (2 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 167522 167374 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.675220000000e+05, best bound 1.675220000000e+05, gap 0.0000%
=================== for P=15
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros
Model fingerprint: 0xcd36c397
Variable types: 0 continuous, 6448 integer (6448 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 3e+03]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3201 rows and 6405 columns
Presolve time: 0.01s
Presolved: 24 rows, 43 columns, 100 nonzeros
Variable types: 0 continuous, 43 integer (43 binary)
Found heuristic solution: objective 167443.00000
Root relaxation: objective 1.675910e+05, 1 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 167591.00000 167591.000 0.00% - 0s
Explored 1 nodes (1 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 167591 167443 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.675910000000e+05, best bound 1.675910000000e+05, gap 0.0000%
=================== for P=16 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros Model fingerprint: 0x354d63a9 Variable types: 0 continuous, 6448 integer (6448 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 3e+03] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3201 rows and 6405 columns Presolve time: 0.01s Presolved: 24 rows, 43 columns, 100 nonzeros Variable types: 0 continuous, 43 integer (43 binary) Found heuristic solution: objective 167605.00000 Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units) Thread count was 4 (of 4 available processors) Solution count 2: 167605 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.676050000000e+05, best bound 1.676050000000e+05, gap 0.0000%
=================== for P=17 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros Model fingerprint: 0xe7e25a44 Variable types: 0 continuous, 6448 integer (6448 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 3e+03] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3203 rows and 6407 columns Presolve time: 0.01s Presolved: 22 rows, 41 columns, 90 nonzeros Found heuristic solution: objective 167606.00000 Variable types: 0 continuous, 41 integer (41 binary) Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.01 work units) Thread count was 4 (of 4 available processors) Solution count 2: 167606 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=18 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros Model fingerprint: 0x85b62fa8 Variable types: 0 continuous, 6448 integer (6448 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 3e+03] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3210 rows and 6414 columns Presolve time: 0.01s Presolved: 15 rows, 34 columns, 62 nonzeros Found heuristic solution: objective 167606.00000 Variable types: 0 continuous, 34 integer (34 binary) Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.01 work units) Thread count was 4 (of 4 available processors) Solution count 2: 167606 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=19 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros Model fingerprint: 0xb50fdd7a Variable types: 0 continuous, 6448 integer (6448 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 3e+03] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3225 rows and 6448 columns Presolve time: 0.03s Presolve: All rows and columns removed Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.00 work units) Thread count was 1 (of 4 available processors) Solution count 2: 167606 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=20 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros Model fingerprint: 0x8394f29b Variable types: 0 continuous, 6448 integer (6448 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 3e+03] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3225 rows and 6448 columns Presolve time: 0.01s Presolve: All rows and columns removed Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units) Thread count was 1 (of 4 available processors) Solution count 2: 167606 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=21 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros Model fingerprint: 0x5da5f73e Variable types: 0 continuous, 6448 integer (6448 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 3e+03] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3225 rows and 6448 columns Presolve time: 0.01s Presolve: All rows and columns removed Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units) Thread count was 1 (of 4 available processors) Solution count 2: 167606 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=22 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros Model fingerprint: 0x25d04cef Variable types: 0 continuous, 6448 integer (6448 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 3e+03] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3225 rows and 6448 columns Presolve time: 0.01s Presolve: All rows and columns removed Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units) Thread count was 1 (of 4 available processors) Solution count 2: 167606 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=23 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros Model fingerprint: 0x0c7cae08 Variable types: 0 continuous, 6448 integer (6448 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 3e+03] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3225 rows and 6448 columns Presolve time: 0.01s Presolve: All rows and columns removed Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units) Thread count was 1 (of 4 available processors) Solution count 2: 167606 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=24 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros Model fingerprint: 0x53d33e31 Variable types: 0 continuous, 6448 integer (6448 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 3e+03] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3225 rows and 6448 columns Presolve time: 0.01s Presolve: All rows and columns removed Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units) Thread count was 1 (of 4 available processors) Solution count 2: 167606 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=25 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros Model fingerprint: 0x7ea4a4ef Variable types: 0 continuous, 6448 integer (6448 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 3e+03] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3225 rows and 6448 columns Presolve time: 0.10s Presolve: All rows and columns removed Explored 0 nodes (0 simplex iterations) in 0.12 seconds (0.00 work units) Thread count was 1 (of 4 available processors) Solution count 2: 167606 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=26 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros Model fingerprint: 0x5c8dcf4c Variable types: 0 continuous, 6448 integer (6448 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 3e+03] Bounds range [1e+00, 1e+00] RHS range [3e+01, 3e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3225 rows and 6448 columns Presolve time: 0.01s Presolve: All rows and columns removed Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units) Thread count was 1 (of 4 available processors) Solution count 2: 167606 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=27 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros Model fingerprint: 0x14058442 Variable types: 0 continuous, 6448 integer (6448 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 3e+03] Bounds range [1e+00, 1e+00] RHS range [3e+01, 3e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3225 rows and 6448 columns Presolve time: 0.01s Presolve: All rows and columns removed Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units) Thread count was 1 (of 4 available processors) Solution count 2: 167606 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
=================== for P=28 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3225 rows, 6448 columns and 13191 nonzeros Model fingerprint: 0x7fc3c448 Variable types: 0 continuous, 6448 integer (6448 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 3e+03] Bounds range [1e+00, 1e+00] RHS range [3e+01, 3e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3225 rows and 6448 columns Presolve time: 0.01s Presolve: All rows and columns removed Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units) Thread count was 1 (of 4 available processors) Solution count 2: 167606 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.676060000000e+05, best bound 1.676060000000e+05, gap 0.0000%
boundary = SBC_FD.envelope # .envelope gives you the bounding rectangle of given GeoDataFrame.
boundary.bounds
| minx | miny | maxx | maxy | |
|---|---|---|---|---|
| 4 | -61331.613 | -401270.1778 | 50847.5684 | -323367.7559 |
minx, miny, maxx, maxy = boundary.loc[4].bounds
print(minx, miny, maxx, maxy)
-61331.61300000176 -401270.1777999997 50847.56839999929 -323367.7559000002
from shapely.geometry import Point
# Here, we are going to create fishnet points.
# Fishnet points are points spaced with an equal interval.
# You'll see when you see the output!
# Define the interval between points
#### Note: Adjust interval value as needed for lab question 2
def create_fishnet(interval):
# Create arrays of x and y coordinates using np.arange
x_coords = np.arange(minx, maxx, interval)
y_coords = np.arange(miny, maxy, interval)
# Create a list to store the points
fishnet_points = []
# Generate points for the fishnet
for y in y_coords:
for x in x_coords:
fishnet_points.append((x, y))
# Print the number of points generated
print("Number of points in the fishnet:", len(fishnet_points))
fishnet_points = gpd.GeoSeries([Point(pt_cd) for pt_cd in fishnet_points])
fishnet_points = fishnet_points[fishnet_points.within(SBC_FD.geometry[4])]
fishnet_points.plot(figsize=(15,5))
return fishnet_points
interval = 5280/5 # default: 5280/5 feet (1 mile / 5 = 0.2 mile)
fishnet_points = create_fishnet(interval)
Number of points in the fishnet: 7918
# Current Coverage
current_coverage = fishnet_points.within(stations.buffer(S).unary_union)
current_coverage = current_coverage.sum()
current_coverage
4065
Note: all the fishnet points will have the same weight, 1.
I = len(fishnet_points)
J = len(stations)
a_i = [1 for i in fishnet_points]
D_ij = np.zeros((I, J))
for i in range (I):
for j in range (J):
D_ij[i][j] = fishnet_points.geometry.iloc[i].distance(stations.geometry.iloc[j])
N_i = {i: [j for j in range(J) if D_ij[i][j] <= S] for i in range(I)}
selecteds = [] # List to store selected stations for each value of p
obj_vals = [] # List to store objective values for each value of p
# Iterate over values of p starting from 3
for p in range(3, len(stations)+1):
print(f"=================== for P={p}") # Print current value of p
# Call solve_mclp function to solve the problem for current value of p
selected_stations, obj_val = solve_mclp(p)
# Append selected stations to the selecteds list
selecteds.append(selected_stations)
# Append objective value to the obj_vals list
obj_vals.append(obj_val)
=================== for P=3
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x389340da
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [3e+00, 3e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 506.0000000
Root relaxation: objective 5.400000e+02, 45 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 540.0000000 540.00000 0.00% - 0s
Explored 1 nodes (45 simplex iterations) in 0.17 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 540 506 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 5.400000000000e+02, best bound 5.400000000000e+02, gap 0.0000%
=================== for P=4
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x7e244e0c
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [4e+00, 4e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 582.0000000
Root relaxation: objective 7.040000e+02, 46 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 704.0000000 704.00000 0.00% - 0s
Explored 1 nodes (46 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 704 582 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 7.040000000000e+02, best bound 7.040000000000e+02, gap 0.0000%
=================== for P=5
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xd5c0d085
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [5e+00, 5e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 675.0000000
Root relaxation: objective 8.550000e+02, 43 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 855.0000000 855.00000 0.00% - 0s
Explored 1 nodes (43 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 855 675 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 8.550000000000e+02, best bound 8.550000000000e+02, gap 0.0000%
=================== for P=6
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xe2dcaec6
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [6e+00, 6e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 746.0000000
Root relaxation: objective 1.005000e+03, 39 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1005.0000000 1005.00000 0.00% - 0s
Explored 1 nodes (39 simplex iterations) in 0.09 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1005 746 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.005000000000e+03, best bound 1.005000000000e+03, gap 0.0000%
=================== for P=7
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x03031656
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [7e+00, 7e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 929.0000000
Root relaxation: objective 1.146000e+03, 38 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1146.0000000 1146.00000 0.00% - 0s
Explored 1 nodes (38 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1146 929 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.146000000000e+03, best bound 1.146000000000e+03, gap 0.0000%
=================== for P=8
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xe1716b61
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [8e+00, 8e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1086.0000000
Root relaxation: objective 1.270000e+03, 30 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1270.0000000 1270.00000 0.00% - 0s
Explored 1 nodes (30 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1270 1086 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.270000000000e+03, best bound 1.270000000000e+03, gap 0.0000%
=================== for P=9
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x0064714e
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [9e+00, 9e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1177.0000000
Root relaxation: objective 1.384000e+03, 30 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1384.0000000 1384.00000 0.00% - 0s
Explored 1 nodes (30 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1384 1177 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.384000000000e+03, best bound 1.384000000000e+03, gap 0.0000%
=================== for P=10
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x59a2cd6c
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1291.0000000
Root relaxation: objective 1.475000e+03, 27 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1475.0000000 1475.00000 0.00% - 0s
Explored 1 nodes (27 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1475 1291 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.475000000000e+03, best bound 1.475000000000e+03, gap 0.0000%
=================== for P=11
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x09995fa2
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1433.0000000
Root relaxation: objective 1.564000e+03, 27 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1564.0000000 1564.00000 0.00% - 0s
Explored 1 nodes (27 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1564 1433 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.564000000000e+03, best bound 1.564000000000e+03, gap 0.0000%
=================== for P=12
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x76eb931e
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1493.0000000
Root relaxation: objective 1.647000e+03, 27 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1647.0000000 1647.00000 0.00% - 0s
Explored 1 nodes (27 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1647 1493 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.647000000000e+03, best bound 1.647000000000e+03, gap 0.0000%
=================== for P=13
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x9f43fd0d
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1591.0000000
Root relaxation: objective 1.715000e+03, 18 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1715.0000000 1715.00000 0.00% - 0s
Explored 1 nodes (18 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1715 1591 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.715000000000e+03, best bound 1.715000000000e+03, gap 0.0000%
=================== for P=14
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x96e00db9
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1611.0000000
Root relaxation: objective 1.743000e+03, 17 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1743.0000000 1743.00000 0.00% - 0s
Explored 1 nodes (17 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1743 1611 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.743000000000e+03, best bound 1.743000000000e+03, gap 0.0000%
=================== for P=15
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xb856d7f5
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1646.0000000
Root relaxation: objective 1.763000e+03, 14 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1763.0000000 1763.00000 0.00% - 0s
Explored 1 nodes (14 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1763 1646 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.763000000000e+03, best bound 1.763000000000e+03, gap 0.0000%
=================== for P=16
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x850efa85
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1714.0000000
Root relaxation: objective 1.780000e+03, 8 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1780.0000000 1780.00000 0.00% - 0s
Explored 1 nodes (8 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1780 1714 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.780000000000e+03, best bound 1.780000000000e+03, gap 0.0000%
=================== for P=17
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x924aa403
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1789.0000000
Root relaxation: cutoff, 3 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 cutoff 0 1789.00000 1789.00000 0.00% - 0s
Explored 1 nodes (3 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 2: 1789 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.789000000000e+03, best bound 1.789000000000e+03, gap 0.0000%
=================== for P=18
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x9fdd0b2d
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1793.0000000
Root relaxation: infeasible, 1 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 infeasible 0 1793.00000 1793.00000 0.00% - 0s
Explored 1 nodes (1 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 2: 1793 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.793000000000e+03, best bound 1.793000000000e+03, gap 0.0000%
=================== for P=19
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xbefdbbc8
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1797.0000000
Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 2: 1797 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=20
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xc70b4648
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3261 rows and 6540 columns
Presolve time: 0.02s
Presolved: 44 rows, 68 columns, 192 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 68 integer (68 binary)
Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 2: 1797 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=21
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xc686342d
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3264 rows and 6543 columns
Presolve time: 0.01s
Presolved: 41 rows, 65 columns, 174 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 65 integer (65 binary)
Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 2: 1797 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=22
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x1cd35457
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3272 rows and 6551 columns
Presolve time: 0.01s
Presolved: 33 rows, 57 columns, 134 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 57 integer (57 binary)
Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 2: 1797 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=23
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x252332b2
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3285 rows and 6564 columns
Presolve time: 0.01s
Presolved: 20 rows, 44 columns, 82 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 44 integer (44 binary)
Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 2: 1797 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=24
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x69bf8981
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed
Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)
Solution count 2: 1797 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=25
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xa3528c1e
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed
Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)
Solution count 2: 1797 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=26
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x6841d82b
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed
Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)
Solution count 2: 1797 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=27
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x027cece1
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.02s
Presolve: All rows and columns removed
Explored 0 nodes (0 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)
Solution count 2: 1797 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=28
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x1d894e10
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed
Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)
Solution count 2: 1797 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
optimize_and_evaluate(demand_block=False)
=================== for P=3
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x389340da
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [3e+00, 3e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 506.0000000
Root relaxation: objective 5.400000e+02, 45 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 540.0000000 540.00000 0.00% - 0s
Explored 1 nodes (45 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 540 506 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 5.400000000000e+02, best bound 5.400000000000e+02, gap 0.0000%
=================== for P=4
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x7e244e0c
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [4e+00, 4e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 582.0000000
Root relaxation: objective 7.040000e+02, 46 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 704.0000000 704.00000 0.00% - 0s
Explored 1 nodes (46 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 704 582 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 7.040000000000e+02, best bound 7.040000000000e+02, gap 0.0000%
=================== for P=5
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xd5c0d085
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [5e+00, 5e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 675.0000000
Root relaxation: objective 8.550000e+02, 43 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 855.0000000 855.00000 0.00% - 0s
Explored 1 nodes (43 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 855 675 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 8.550000000000e+02, best bound 8.550000000000e+02, gap 0.0000%
=================== for P=6
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xe2dcaec6
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [6e+00, 6e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 746.0000000
Root relaxation: objective 1.005000e+03, 39 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1005.0000000 1005.00000 0.00% - 0s
Explored 1 nodes (39 simplex iterations) in 0.08 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1005 746 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.005000000000e+03, best bound 1.005000000000e+03, gap 0.0000%
=================== for P=7
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x03031656
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [7e+00, 7e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 929.0000000
Root relaxation: objective 1.146000e+03, 38 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1146.0000000 1146.00000 0.00% - 0s
Explored 1 nodes (38 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1146 929 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.146000000000e+03, best bound 1.146000000000e+03, gap 0.0000%
=================== for P=8
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xe1716b61
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [8e+00, 8e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.03s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1086.0000000
Root relaxation: objective 1.270000e+03, 30 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1270.0000000 1270.00000 0.00% - 0s
Explored 1 nodes (30 simplex iterations) in 0.09 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1270 1086 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.270000000000e+03, best bound 1.270000000000e+03, gap 0.0000%
=================== for P=9
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x0064714e
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [9e+00, 9e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1177.0000000
Root relaxation: objective 1.384000e+03, 30 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1384.0000000 1384.00000 0.00% - 0s
Explored 1 nodes (30 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1384 1177 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.384000000000e+03, best bound 1.384000000000e+03, gap 0.0000%
=================== for P=10
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x59a2cd6c
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1291.0000000
Root relaxation: objective 1.475000e+03, 27 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1475.0000000 1475.00000 0.00% - 0s
Explored 1 nodes (27 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1475 1291 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.475000000000e+03, best bound 1.475000000000e+03, gap 0.0000%
=================== for P=11
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x09995fa2
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1433.0000000
Root relaxation: objective 1.564000e+03, 27 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1564.0000000 1564.00000 0.00% - 0s
Explored 1 nodes (27 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1564 1433 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.564000000000e+03, best bound 1.564000000000e+03, gap 0.0000%
=================== for P=12
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x76eb931e
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1493.0000000
Root relaxation: objective 1.647000e+03, 27 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1647.0000000 1647.00000 0.00% - 0s
Explored 1 nodes (27 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1647 1493 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.647000000000e+03, best bound 1.647000000000e+03, gap 0.0000%
=================== for P=13
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x9f43fd0d
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1591.0000000
Root relaxation: objective 1.715000e+03, 18 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1715.0000000 1715.00000 0.00% - 0s
Explored 1 nodes (18 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1715 1591 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.715000000000e+03, best bound 1.715000000000e+03, gap 0.0000%
=================== for P=14
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x96e00db9
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1611.0000000
Root relaxation: objective 1.743000e+03, 17 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1743.0000000 1743.00000 0.00% - 0s
Explored 1 nodes (17 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1743 1611 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.743000000000e+03, best bound 1.743000000000e+03, gap 0.0000%
=================== for P=15
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xb856d7f5
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1646.0000000
Root relaxation: objective 1.763000e+03, 14 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1763.0000000 1763.00000 0.00% - 0s
Explored 1 nodes (14 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1763 1646 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.763000000000e+03, best bound 1.763000000000e+03, gap 0.0000%
=================== for P=16
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x850efa85
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1714.0000000
Root relaxation: objective 1.780000e+03, 8 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1780.0000000 1780.00000 0.00% - 0s
Explored 1 nodes (8 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1780 1714 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.780000000000e+03, best bound 1.780000000000e+03, gap 0.0000%
=================== for P=17
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x924aa403
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1789.0000000
Root relaxation: cutoff, 3 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 cutoff 0 1789.00000 1789.00000 0.00% - 0s
Explored 1 nodes (3 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 2: 1789 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.789000000000e+03, best bound 1.789000000000e+03, gap 0.0000%
=================== for P=18
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x9fdd0b2d
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1793.0000000
Root relaxation: infeasible, 1 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 infeasible 0 1793.00000 1793.00000 0.00% - 0s
Explored 1 nodes (1 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 2: 1793 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.793000000000e+03, best bound 1.793000000000e+03, gap 0.0000%
=================== for P=19 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros Model fingerprint: 0xbefdbbc8 Variable types: 0 continuous, 6608 integer (6608 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 1e+00] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3260 rows and 6539 columns Presolve time: 0.02s Presolved: 45 rows, 69 columns, 199 nonzeros Variable types: 0 continuous, 69 integer (69 binary) Found heuristic solution: objective 1797.0000000 Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units) Thread count was 4 (of 4 available processors) Solution count 2: 1797 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=20 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros Model fingerprint: 0xc70b4648 Variable types: 0 continuous, 6608 integer (6608 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 1e+00] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3261 rows and 6540 columns Presolve time: 0.01s Presolved: 44 rows, 68 columns, 192 nonzeros Found heuristic solution: objective 1797.0000000 Variable types: 0 continuous, 68 integer (68 binary) Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.00 work units) Thread count was 4 (of 4 available processors) Solution count 2: 1797 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=21 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros Model fingerprint: 0xc686342d Variable types: 0 continuous, 6608 integer (6608 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 1e+00] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3264 rows and 6543 columns Presolve time: 0.02s Presolved: 41 rows, 65 columns, 174 nonzeros Found heuristic solution: objective 1797.0000000 Variable types: 0 continuous, 65 integer (65 binary) Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units) Thread count was 4 (of 4 available processors) Solution count 2: 1797 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=22 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros Model fingerprint: 0x1cd35457 Variable types: 0 continuous, 6608 integer (6608 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 1e+00] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3272 rows and 6551 columns Presolve time: 0.01s Presolved: 33 rows, 57 columns, 134 nonzeros Found heuristic solution: objective 1797.0000000 Variable types: 0 continuous, 57 integer (57 binary) Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units) Thread count was 4 (of 4 available processors) Solution count 2: 1797 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=23 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros Model fingerprint: 0x252332b2 Variable types: 0 continuous, 6608 integer (6608 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 1e+00] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3285 rows and 6564 columns Presolve time: 0.01s Presolved: 20 rows, 44 columns, 82 nonzeros Found heuristic solution: objective 1797.0000000 Variable types: 0 continuous, 44 integer (44 binary) Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.00 work units) Thread count was 4 (of 4 available processors) Solution count 2: 1797 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=24 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros Model fingerprint: 0x69bf8981 Variable types: 0 continuous, 6608 integer (6608 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 1e+00] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3305 rows and 6608 columns Presolve time: 0.02s Presolve: All rows and columns removed Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.00 work units) Thread count was 1 (of 4 available processors) Solution count 2: 1797 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=25 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros Model fingerprint: 0xa3528c1e Variable types: 0 continuous, 6608 integer (6608 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 1e+00] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3305 rows and 6608 columns Presolve time: 0.01s Presolve: All rows and columns removed Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units) Thread count was 1 (of 4 available processors) Solution count 2: 1797 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=26 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros Model fingerprint: 0x6841d82b Variable types: 0 continuous, 6608 integer (6608 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 1e+00] Bounds range [1e+00, 1e+00] RHS range [3e+01, 3e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3305 rows and 6608 columns Presolve time: 0.01s Presolve: All rows and columns removed Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.00 work units) Thread count was 1 (of 4 available processors) Solution count 2: 1797 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=27 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros Model fingerprint: 0x027cece1 Variable types: 0 continuous, 6608 integer (6608 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 1e+00] Bounds range [1e+00, 1e+00] RHS range [3e+01, 3e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3305 rows and 6608 columns Presolve time: 0.01s Presolve: All rows and columns removed Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units) Thread count was 1 (of 4 available processors) Solution count 2: 1797 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=28 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros Model fingerprint: 0x1d894e10 Variable types: 0 continuous, 6608 integer (6608 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 1e+00] Bounds range [1e+00, 1e+00] RHS range [3e+01, 3e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3305 rows and 6608 columns Presolve time: 0.01s Presolve: All rows and columns removed Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units) Thread count was 1 (of 4 available processors) Solution count 2: 1797 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
interval = 5280 # default: 5280/5 feet (1 mile / 5 = 0.2 mile)
fishnet_points = create_fishnet(interval)
Number of points in the fishnet: 330
selecteds = [] # List to store selected stations for each value of p
obj_vals = [] # List to store objective values for each value of p
# Iterate over values of p starting from 3
for p in range(3, len(stations)+1):
print(f"=================== for P={p}") # Print current value of p
# Call solve_mclp function to solve the problem for current value of p
selected_stations, obj_val = solve_mclp(p)
# Append selected stations to the selecteds list
selecteds.append(selected_stations)
# Append objective value to the obj_vals list
obj_vals.append(obj_val)
=================== for P=3
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x389340da
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [3e+00, 3e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 506.0000000
Root relaxation: objective 5.400000e+02, 45 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 540.0000000 540.00000 0.00% - 0s
Explored 1 nodes (45 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 540 506 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 5.400000000000e+02, best bound 5.400000000000e+02, gap 0.0000%
=================== for P=4
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x7e244e0c
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [4e+00, 4e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 582.0000000
Root relaxation: objective 7.040000e+02, 46 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 704.0000000 704.00000 0.00% - 0s
Explored 1 nodes (46 simplex iterations) in 0.08 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 704 582 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 7.040000000000e+02, best bound 7.040000000000e+02, gap 0.0000%
=================== for P=5
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xd5c0d085
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [5e+00, 5e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.03s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 675.0000000
Root relaxation: objective 8.550000e+02, 43 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 855.0000000 855.00000 0.00% - 0s
Explored 1 nodes (43 simplex iterations) in 0.10 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 855 675 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 8.550000000000e+02, best bound 8.550000000000e+02, gap 0.0000%
=================== for P=6
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xe2dcaec6
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [6e+00, 6e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.03s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 746.0000000
Root relaxation: objective 1.005000e+03, 39 iterations, 0.01 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1005.0000000 1005.00000 0.00% - 0s
Explored 1 nodes (39 simplex iterations) in 0.13 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1005 746 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.005000000000e+03, best bound 1.005000000000e+03, gap 0.0000%
=================== for P=7
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x03031656
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [7e+00, 7e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 929.0000000
Root relaxation: objective 1.146000e+03, 38 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1146.0000000 1146.00000 0.00% - 0s
Explored 1 nodes (38 simplex iterations) in 0.19 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1146 929 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.146000000000e+03, best bound 1.146000000000e+03, gap 0.0000%
=================== for P=8
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xe1716b61
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [8e+00, 8e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1086.0000000
Root relaxation: objective 1.270000e+03, 30 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1270.0000000 1270.00000 0.00% - 0s
Explored 1 nodes (30 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1270 1086 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.270000000000e+03, best bound 1.270000000000e+03, gap 0.0000%
=================== for P=9
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x0064714e
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [9e+00, 9e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1177.0000000
Root relaxation: objective 1.384000e+03, 30 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1384.0000000 1384.00000 0.00% - 0s
Explored 1 nodes (30 simplex iterations) in 0.08 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1384 1177 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.384000000000e+03, best bound 1.384000000000e+03, gap 0.0000%
=================== for P=10
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x59a2cd6c
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1291.0000000
Root relaxation: objective 1.475000e+03, 27 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1475.0000000 1475.00000 0.00% - 0s
Explored 1 nodes (27 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1475 1291 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.475000000000e+03, best bound 1.475000000000e+03, gap 0.0000%
=================== for P=11
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x09995fa2
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1433.0000000
Root relaxation: objective 1.564000e+03, 27 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1564.0000000 1564.00000 0.00% - 0s
Explored 1 nodes (27 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1564 1433 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.564000000000e+03, best bound 1.564000000000e+03, gap 0.0000%
=================== for P=12
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x76eb931e
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1493.0000000
Root relaxation: objective 1.647000e+03, 27 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1647.0000000 1647.00000 0.00% - 0s
Explored 1 nodes (27 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1647 1493 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.647000000000e+03, best bound 1.647000000000e+03, gap 0.0000%
=================== for P=13
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x9f43fd0d
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1591.0000000
Root relaxation: objective 1.715000e+03, 18 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1715.0000000 1715.00000 0.00% - 0s
Explored 1 nodes (18 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1715 1591 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.715000000000e+03, best bound 1.715000000000e+03, gap 0.0000%
=================== for P=14
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x96e00db9
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1611.0000000
Root relaxation: objective 1.743000e+03, 17 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1743.0000000 1743.00000 0.00% - 0s
Explored 1 nodes (17 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1743 1611 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.743000000000e+03, best bound 1.743000000000e+03, gap 0.0000%
=================== for P=15
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xb856d7f5
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1646.0000000
Root relaxation: objective 1.763000e+03, 14 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1763.0000000 1763.00000 0.00% - 0s
Explored 1 nodes (14 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1763 1646 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.763000000000e+03, best bound 1.763000000000e+03, gap 0.0000%
=================== for P=16
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x850efa85
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1714.0000000
Root relaxation: objective 1.780000e+03, 8 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1780.0000000 1780.00000 0.00% - 0s
Explored 1 nodes (8 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1780 1714 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.780000000000e+03, best bound 1.780000000000e+03, gap 0.0000%
=================== for P=17
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x924aa403
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1789.0000000
Root relaxation: cutoff, 3 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 cutoff 0 1789.00000 1789.00000 0.00% - 0s
Explored 1 nodes (3 simplex iterations) in 0.10 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 2: 1789 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.789000000000e+03, best bound 1.789000000000e+03, gap 0.0000%
=================== for P=18
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x9fdd0b2d
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1793.0000000
Root relaxation: infeasible, 1 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 infeasible 0 1793.00000 1793.00000 0.00% - 0s
Explored 1 nodes (1 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 2: 1793 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.793000000000e+03, best bound 1.793000000000e+03, gap 0.0000%
=================== for P=19
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xbefdbbc8
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.04s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1797.0000000
Explored 0 nodes (0 simplex iterations) in 0.12 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 2: 1797 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=20
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xc70b4648
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3261 rows and 6540 columns
Presolve time: 0.02s
Presolved: 44 rows, 68 columns, 192 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 68 integer (68 binary)
Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 2: 1797 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=21
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xc686342d
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3264 rows and 6543 columns
Presolve time: 0.02s
Presolved: 41 rows, 65 columns, 174 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 65 integer (65 binary)
Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 2: 1797 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=22
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x1cd35457
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3272 rows and 6551 columns
Presolve time: 0.01s
Presolved: 33 rows, 57 columns, 134 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 57 integer (57 binary)
Explored 0 nodes (0 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 2: 1797 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=23
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x252332b2
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3285 rows and 6564 columns
Presolve time: 0.01s
Presolved: 20 rows, 44 columns, 82 nonzeros
Found heuristic solution: objective 1797.0000000
Variable types: 0 continuous, 44 integer (44 binary)
Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 2: 1797 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=24
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x69bf8981
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed
Explored 0 nodes (0 simplex iterations) in 0.15 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)
Solution count 2: 1797 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=25
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xa3528c1e
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed
Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)
Solution count 2: 1797 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=26
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x6841d82b
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed
Explored 0 nodes (0 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)
Solution count 2: 1797 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=27
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x027cece1
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed
Explored 0 nodes (0 simplex iterations) in 0.02 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)
Solution count 2: 1797 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=28
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x1d894e10
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [3e+01, 3e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3305 rows and 6608 columns
Presolve time: 0.01s
Presolve: All rows and columns removed
Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 1 (of 4 available processors)
Solution count 2: 1797 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
optimize_and_evaluate(demand_block=False)
=================== for P=3
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x389340da
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [3e+00, 3e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 506.0000000
Root relaxation: objective 5.400000e+02, 45 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 540.0000000 540.00000 0.00% - 0s
Explored 1 nodes (45 simplex iterations) in 0.15 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 540 506 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 5.400000000000e+02, best bound 5.400000000000e+02, gap 0.0000%
=================== for P=4
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x7e244e0c
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [4e+00, 4e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.03s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 582.0000000
Root relaxation: objective 7.040000e+02, 46 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 704.0000000 704.00000 0.00% - 0s
Explored 1 nodes (46 simplex iterations) in 0.07 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 704 582 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 7.040000000000e+02, best bound 7.040000000000e+02, gap 0.0000%
=================== for P=5
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xd5c0d085
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [5e+00, 5e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 675.0000000
Root relaxation: objective 8.550000e+02, 43 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 855.0000000 855.00000 0.00% - 0s
Explored 1 nodes (43 simplex iterations) in 0.08 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 855 675 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 8.550000000000e+02, best bound 8.550000000000e+02, gap 0.0000%
=================== for P=6
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xe2dcaec6
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [6e+00, 6e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 746.0000000
Root relaxation: objective 1.005000e+03, 39 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1005.0000000 1005.00000 0.00% - 0s
Explored 1 nodes (39 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1005 746 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.005000000000e+03, best bound 1.005000000000e+03, gap 0.0000%
=================== for P=7
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x03031656
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [7e+00, 7e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 929.0000000
Root relaxation: objective 1.146000e+03, 38 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1146.0000000 1146.00000 0.00% - 0s
Explored 1 nodes (38 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1146 929 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.146000000000e+03, best bound 1.146000000000e+03, gap 0.0000%
=================== for P=8
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xe1716b61
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [8e+00, 8e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1086.0000000
Root relaxation: objective 1.270000e+03, 30 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1270.0000000 1270.00000 0.00% - 0s
Explored 1 nodes (30 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1270 1086 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.270000000000e+03, best bound 1.270000000000e+03, gap 0.0000%
=================== for P=9
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x0064714e
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [9e+00, 9e+00]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1177.0000000
Root relaxation: objective 1.384000e+03, 30 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1384.0000000 1384.00000 0.00% - 0s
Explored 1 nodes (30 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1384 1177 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.384000000000e+03, best bound 1.384000000000e+03, gap 0.0000%
=================== for P=10
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x59a2cd6c
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1291.0000000
Root relaxation: objective 1.475000e+03, 27 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1475.0000000 1475.00000 0.00% - 0s
Explored 1 nodes (27 simplex iterations) in 0.06 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1475 1291 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.475000000000e+03, best bound 1.475000000000e+03, gap 0.0000%
=================== for P=11
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x09995fa2
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1433.0000000
Root relaxation: objective 1.564000e+03, 27 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1564.0000000 1564.00000 0.00% - 0s
Explored 1 nodes (27 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1564 1433 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.564000000000e+03, best bound 1.564000000000e+03, gap 0.0000%
=================== for P=12
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x76eb931e
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1493.0000000
Root relaxation: objective 1.647000e+03, 27 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1647.0000000 1647.00000 0.00% - 0s
Explored 1 nodes (27 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1647 1493 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.647000000000e+03, best bound 1.647000000000e+03, gap 0.0000%
=================== for P=13
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x9f43fd0d
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1591.0000000
Root relaxation: objective 1.715000e+03, 18 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1715.0000000 1715.00000 0.00% - 0s
Explored 1 nodes (18 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1715 1591 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.715000000000e+03, best bound 1.715000000000e+03, gap 0.0000%
=================== for P=14
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x96e00db9
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [1e+01, 1e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1611.0000000
Root relaxation: objective 1.743000e+03, 17 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1743.0000000 1743.00000 0.00% - 0s
Explored 1 nodes (17 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1743 1611 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.743000000000e+03, best bound 1.743000000000e+03, gap 0.0000%
=================== for P=15
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0xb856d7f5
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.02s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1646.0000000
Root relaxation: objective 1.763000e+03, 14 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1763.0000000 1763.00000 0.00% - 0s
Explored 1 nodes (14 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1763 1646 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.763000000000e+03, best bound 1.763000000000e+03, gap 0.0000%
=================== for P=16
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x850efa85
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1714.0000000
Root relaxation: objective 1.780000e+03, 8 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 1780.0000000 1780.00000 0.00% - 0s
Explored 1 nodes (8 simplex iterations) in 0.05 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 3: 1780 1714 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.780000000000e+03, best bound 1.780000000000e+03, gap 0.0000%
=================== for P=17
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x924aa403
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1789.0000000
Root relaxation: cutoff, 3 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 cutoff 0 1789.00000 1789.00000 0.00% - 0s
Explored 1 nodes (3 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 2: 1789 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.789000000000e+03, best bound 1.789000000000e+03, gap 0.0000%
=================== for P=18
Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86])
CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros
Model fingerprint: 0x9fdd0b2d
Variable types: 0 continuous, 6608 integer (6608 binary)
Coefficient statistics:
Matrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [1e+00, 1e+00]
RHS range [2e+01, 2e+01]
Found heuristic solution: objective -0.0000000
Presolve removed 3260 rows and 6539 columns
Presolve time: 0.01s
Presolved: 45 rows, 69 columns, 199 nonzeros
Variable types: 0 continuous, 69 integer (69 binary)
Found heuristic solution: objective 1793.0000000
Root relaxation: infeasible, 1 iterations, 0.00 seconds (0.00 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 infeasible 0 1793.00000 1793.00000 0.00% - 0s
Explored 1 nodes (1 simplex iterations) in 0.04 seconds (0.00 work units)
Thread count was 4 (of 4 available processors)
Solution count 2: 1793 -0
Optimal solution found (tolerance 1.00e-04)
Best objective 1.793000000000e+03, best bound 1.793000000000e+03, gap 0.0000%
=================== for P=19 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros Model fingerprint: 0xbefdbbc8 Variable types: 0 continuous, 6608 integer (6608 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 1e+00] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3260 rows and 6539 columns Presolve time: 0.01s Presolved: 45 rows, 69 columns, 199 nonzeros Variable types: 0 continuous, 69 integer (69 binary) Found heuristic solution: objective 1797.0000000 Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units) Thread count was 4 (of 4 available processors) Solution count 2: 1797 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=20 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros Model fingerprint: 0xc70b4648 Variable types: 0 continuous, 6608 integer (6608 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 1e+00] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3261 rows and 6540 columns Presolve time: 0.01s Presolved: 44 rows, 68 columns, 192 nonzeros Found heuristic solution: objective 1797.0000000 Variable types: 0 continuous, 68 integer (68 binary) Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units) Thread count was 4 (of 4 available processors) Solution count 2: 1797 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=21 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros Model fingerprint: 0xc686342d Variable types: 0 continuous, 6608 integer (6608 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 1e+00] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3264 rows and 6543 columns Presolve time: 0.02s Presolved: 41 rows, 65 columns, 174 nonzeros Found heuristic solution: objective 1797.0000000 Variable types: 0 continuous, 65 integer (65 binary) Explored 0 nodes (0 simplex iterations) in 0.05 seconds (0.00 work units) Thread count was 4 (of 4 available processors) Solution count 2: 1797 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=22 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros Model fingerprint: 0x1cd35457 Variable types: 0 continuous, 6608 integer (6608 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 1e+00] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3272 rows and 6551 columns Presolve time: 0.02s Presolved: 33 rows, 57 columns, 134 nonzeros Found heuristic solution: objective 1797.0000000 Variable types: 0 continuous, 57 integer (57 binary) Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units) Thread count was 4 (of 4 available processors) Solution count 2: 1797 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=23 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros Model fingerprint: 0x252332b2 Variable types: 0 continuous, 6608 integer (6608 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 1e+00] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3285 rows and 6564 columns Presolve time: 0.01s Presolved: 20 rows, 44 columns, 82 nonzeros Found heuristic solution: objective 1797.0000000 Variable types: 0 continuous, 44 integer (44 binary) Explored 0 nodes (0 simplex iterations) in 0.04 seconds (0.00 work units) Thread count was 4 (of 4 available processors) Solution count 2: 1797 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=24 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros Model fingerprint: 0x69bf8981 Variable types: 0 continuous, 6608 integer (6608 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 1e+00] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3305 rows and 6608 columns Presolve time: 0.01s Presolve: All rows and columns removed Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units) Thread count was 1 (of 4 available processors) Solution count 2: 1797 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=25 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros Model fingerprint: 0xa3528c1e Variable types: 0 continuous, 6608 integer (6608 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 1e+00] Bounds range [1e+00, 1e+00] RHS range [2e+01, 2e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3305 rows and 6608 columns Presolve time: 0.01s Presolve: All rows and columns removed Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units) Thread count was 1 (of 4 available processors) Solution count 2: 1797 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=26 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros Model fingerprint: 0x6841d82b Variable types: 0 continuous, 6608 integer (6608 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 1e+00] Bounds range [1e+00, 1e+00] RHS range [3e+01, 3e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3305 rows and 6608 columns Presolve time: 0.01s Presolve: All rows and columns removed Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units) Thread count was 1 (of 4 available processors) Solution count 2: 1797 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=27 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros Model fingerprint: 0x027cece1 Variable types: 0 continuous, 6608 integer (6608 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 1e+00] Bounds range [1e+00, 1e+00] RHS range [3e+01, 3e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3305 rows and 6608 columns Presolve time: 0.01s Presolve: All rows and columns removed Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units) Thread count was 1 (of 4 available processors) Solution count 2: 1797 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
=================== for P=28 Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (mac64[x86]) CPU model: Intel(R) Core(TM) i5-5350U CPU @ 1.80GHz Thread count: 2 physical cores, 4 logical processors, using up to 4 threads Optimize a model with 3305 rows, 6608 columns and 6943 nonzeros Model fingerprint: 0x1d894e10 Variable types: 0 continuous, 6608 integer (6608 binary) Coefficient statistics: Matrix range [1e+00, 1e+00] Objective range [1e+00, 1e+00] Bounds range [1e+00, 1e+00] RHS range [3e+01, 3e+01] Found heuristic solution: objective -0.0000000 Presolve removed 3305 rows and 6608 columns Presolve time: 0.01s Presolve: All rows and columns removed Explored 0 nodes (0 simplex iterations) in 0.03 seconds (0.00 work units) Thread count was 1 (of 4 available processors) Solution count 2: 1797 -0 Optimal solution found (tolerance 1.00e-04) Best objective 1.797000000000e+03, best bound 1.797000000000e+03, gap 0.0000%
In Lab 2, we discovered that different Coverage Distance Standard can impact the coverage analysis result.
In Lab 4, we can discover how different demand representation makes difference.
Share your insights about
TIP: you can copy and paste your screenshot into markdown cells
PUT your answer HERE
Current coverage by SBC_FD is excellent in terms of pure coverage, but not so well in terms of cost efficiency. The current coverage is at the end of the Pareto curve shown in scatter plot 1. This means that they are using far more stations than they need to for the coverage they are providing. This can be seen in the flattening of the curve as it approaches the current coverage level. They could reduce the number of stations and get the same amount of coverage and save millions of dollars a year.
When the demand representation was defined using population, there were many overlapping stations placed on the downtown SB area and other population dense regions. At the same time, these coverage areas were not spatially optimized in the sense that many of them were overlapping in order to cover larger populations. When we optimized based on a maximization of fishnet points the locations were largely organized in the middle of the county. This makes sense give that there are the most fishnet points in the center as opposed to coastlines or other more complex regions.